On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree-Reference-Cited by-同舟云学术

On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree

Published:2024-08-30 Issue:17 Volume:12 Page:2704
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Maitreyi Venkatesan¹,Elumalai Suresh¹^ORCID,Ali Akbar²^ORCID,Balachandran Selvaraj³,Saber Hicham²,Attiya Adel A.²⁴^ORCID

Affiliation:

1. Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India

2. Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia

3. Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India

4. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract

The ABS (atom-bond sum-connectivity) index of a graph G is denoted by ABS(G) and is defined as ∑xy∈E(G)(dx+dy)−1(dx+dy−2), where dx represents the degree of the vertex x in G. In this paper, we derive the best possible upper bounds on the ABS index for fixed-order trees possessing a given maximum degree, which provides a solution to the open problem proposed quite recently by Hussain, Liu and Hua.

Funder

University of Ha’il—Saudi Arabia

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/17/2704/pdf

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